Next, we present the constraints of satisfying the ultra-reliable and low-latency requirement of control and non-payload signal delivery while guaranteeing the high-speed payload transmission.
To satisfy the low-latency requirement, control and non-payload packets are typically very short. Therefore, like [1]}, we assume that the fading channel is a quasi-static Rayleigh fading channel over a time slot and changes independently and explore the data rate formula in finite blocklength regime to model the uplink achievable data rate.
Particularly, define the transmit beamformer of the BS towards the UAV at time slot \(t\)  as \(\mathbf {v}(t) \in {\mathbb {C}}^{K}\)  and \(\mathbf {V}(t) = \mathbf {v}(t) \mathbf {v}^{\rm H}(t) \in {\mathbb {R}}^{K \times K}\) . Let \(\mathbf {H}_{\rm B,v}(t) = \mathbf {h}_{\rm B,v}(t) \mathbf {h}_{\rm B,v}^{\rm H}(t)\) , where \({\mathbf {h}_{\rm B,v}(t) = [h_1^{\rm B}(t);\ldots ;h_K^{\rm B}(t)]}\) .
Since \({\rm tr}(\mathbf {A} \mathbf {B}) = {\rm tr}(\mathbf {B} \mathbf {A})\)  for matrices \(\mathbf {A}\) , \(\mathbf {B}\)  of compatible dimensions, we have \(|\mathbf {h}_{\rm B,v}^{\rm H}(t)\mathbf {v}(t)|^2 =\)  \((\mathbf {h}_{\rm B,v}^{\rm H}(t)\mathbf {v}(t))^{\rm H}\mathbf {h}_{\rm B,v}^{\rm H}(t)\mathbf {v}(t)=\)  \({\rm tr}(\mathbf {v}^{\rm H}(t) \mathbf {h}_{\rm B,v}(t) \mathbf {h}_{\rm B,v}^{\rm H}(t) \mathbf {v}(t)) = \)  \({\rm tr}(\mathbf {H}_{\rm B,v}(t) \mathbf {V}(t))\) . Thus, given the transmission latency \(\tau \)  and the codeword decoding error probability \(\varepsilon \) , the approximately achievable data rate of the UAV can take the form [1]}:
\(\begin{array}{l}R^{\rm ul}(t; \tau ) \approx W {{\log }_2}( {1 + \frac{{{\rm tr}(\mathbf {H}_{\rm B,v}(t) \mathbf {V}(t))}}{{{N_0}W}}} ) - \\\qquad \qquad \sqrt{\frac{{W{B_u}(t)}}{{\tau }}} {Q^{ - 1}}(\varepsilon ){{\log }_2}e,\end{array}\) 
